Abstract
The aim of this paper is to find all plane curve singularities that are taut resp. pseudotaut. It turns out that this problem coincides with the determination of equisingularly rigid singularities. The latter one is achieved in the irreducible case by explicit construction of nontrivial deformations usiing analytical invariants of the Puiseux expansion introduced by Kasner and Zariski, in the reducible case with a cohomological criterion for the triviality of Wahl's functor ES of equisingular deformations of a resolution. Equisingular rigidity is the same as K-zero- or unimodality with discrete parameter. An application is the determination of all equisingularly rigid double points of surfaces, which are just the stabilizations of equisingularly rigid plane curve singularities.
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Gawlick, T. Taut, pseudotaut and equisingularly rigid singularities. Manuscripta Math 74, 25–38 (1992). https://doi.org/10.1007/BF02567655
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DOI: https://doi.org/10.1007/BF02567655